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Physics Formulas Wiki
Measurement and Units Absolute uncertainty =\Delta x Percent uncertainty =\frac{\Delta x}{x}\times 100\%$ Linear Motion Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. v=v_0+at\ \ \ _{:bc:} x=x_0+v_0t+\frac{1}{2}at^2\ \ \ _{:bc:} v^2=v_0^2+2a(x-x_0)\ \ \ _{:bc:} Formulas with Summary Kinematics and Projectile Motion in 2D Formulas v_x=v\cos\theta v_y=v\sin\theta \tan\theta=v_y/v_x v=\sqrt{v_x^2+v_y^2} v_x=v_{x0}+a_xt x=x_0+v_{x0}t+\frac{1}{2}a_xt^2 v_x^2=v_{x0}^2+2a_x(x-x_0) v_y=v_{y0}+a_yt y=y_0+v_{y0}t+\frac{1}{2}a_yt^2 v_y^2=v_{y0}^2+2a_y(y-y_0) Formulas with Summary In projectile motion, the linear motion equations are valid for each coordinate separately. In three dimensions, this gives three identical sets of equations: v_x=v_{x0}+a_xt x=x+v_{x0}t+\frac{1}{2}a_xt^2 v_x^2=v_{x0}^2+2a_x(x-x_0) The equations for y and z are obtained by making the substitutions x\rightarrow y or x\rightarrow z respectively. Vectors can also be specified by a magnitude and angles. Let \theta be the angle measured with respect to horizontal. In two dimensions we have: v_x=v\cos\theta v_y=v\sin\theta v=\sqrt{v_x^2+v_y^2} Newton's Laws Formulas \sum\mathbf{F}=\mathbf{F_{net}}=m\mathbf{a}\ \ \ _{:bc:} \mathbf{F}_G=m\mathbf{g} \mathbf{F}_{fric}\le\mu \mathbf{F}_N\ \ \ _{:bc:} \mathbf{F}_N=mg\cos\theta \mathbf{F}_{AB}=-\mathbf{F}_{BA} Formulas with Summary \mathbf{F}_G = force of gravity. Let \mathbf{F}_{fric} = force of friction, \mu = coefficient of kinetic friction and F_N = normal force. When the object is sliding \mu=\mu_k is the coefficient of kinetic friction and when the object is at rest \mu=\mu_s is the coefficient of static friction. Note that we always have \mu_k\le\mu_s which means it takes the same or more force to get an object sliding than it does to keep it sliding. Energy and Work Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. W=F\Delta r\cos\theta\ \ \ _{:b:} W=\int_C\mathbf{F}\cdot d\mathbf{r}\ \ \ _{:c:} KE=\frac{1}{2}mv^2\ \ \ _{:bc:} PE_{grav}=mgh\ \ \ _{:bc:} PE_{spring}=\frac{1}{2}kx^2\ \ \ _{:b:} P_{avg}=\frac{W}{\Delta t}\ \ \ _{:b:} P=\frac{dW}{dt}\ \ \ _{:c:} P=Fv\cos\theta\ \ \ _{:b:} P=\mathbf{F}\cdot\mathbf{v}\ \ \ _{:c:} E_{initial}=E_{final} Formulas with Summary The work done on an object that is displaced a distance \Delta r by a force F which makes an angle \theta with the direction of motion is given by W=F\Delta r\cos\theta\ \ \ _{:b:} For an object moved along a curve C , this expression can be expressed as a line integral W=\int_C\mathbf{F}\cdot d\mathbf{r}\ \ \ _{:c:} Momentum Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. \mathbf{p}=m\mathbf{v}\ \ \ _{:bc:} \mathbf{J}=\mathbf{F}\Delta t=\Delta \mathbf{p}\ \ \ _{:b:} \mathbf{J}=\int\mathbf{F}dt=\Delta \mathbf{p}\ \ \ _{:c:} \mathbf{F}=\frac{d\mathbf{p}}{dt}\ \ \ _{:c:} x_{CM}=(m_ax_a+m_bx_b+...)/(m_a+m_b+...) \sum E_i=\sum E_f and \ \sum p_i=\sum p_f (elastic collision) \sum p_i=\sum p_f (inelastic collision) Formulas with Summary Rotational Motion Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. a_c=\frac{v^2}{r}=r\omega^2\ \ \ _{:bc:} T=\frac{1}{f}\ \ \ _{:b:} v=r\omega\ \ \ _{:c:} \omega = \omega_0 +\alpha t\ \ \ _{:c:} \theta=\theta_0+\omega_0t+\frac{1}{2}\alpha t^2\ \ \ _{:c:} \omega=\frac{\Delta \theta}{\Delta t} \alpha =\frac{\Delta \omega}{\Delta t} \omega = 2\pi f \omega^2 = \omega_0^2+2\alpha\Delta\theta Formulas with Summary Torque and Angular Momentum Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. \tau = rF\sin\theta\ \ \ _{:b:} \mathbf{\tau}=\mathbf{r}\times\mathbf{F}\ \ \ _{:c:} \sum\mathbf{\tau} =\mathbf{\tau}_{net}=I\mathbf{\alpha}\ \ \ _{:c:} I=\int r^2dm=\sum mr^2\ \ \ _{:c:} \mathbf{r}_{CM}=\sum m\mathbf{r}/\sum m\ \ \ _{:c:} \mathbf{L}=\mathbf{r}\times\mathbf{p}=I\mathbf{\omega}\ \ \ _{:c:} Gravitation Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. F_G=-\frac{Gm_1m_2}{r^2}\ \ \ _{:b:} U_G=-\frac{Gm_1m_2}{r}\ \ \ _{:b:} Formulas with Summary Static Equilibrium and Elasticity Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. Static equilibrium means \sum\mathbf{F}=0 and \sum\mathbf{\tau}=0 F_s=-kx \Delta L=\frac{1}{E}\frac{F}{A}L_0 \Delta V=-\frac{1}{B}V_0\Delta P Formulas with Summary Fluids Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. \rho=m/V\ \ \ _{:b:} P=F/A\ \ \ _{:b:} P=P_0+\rho g h\ \ \ _{:b:} P_{out}=P_{in}\ \ \ _{:b:} F_{buoy}=\rho_{liquid}V_{object}g\ \ \ _{:b:} A_1v_1=A_2v_2\ \ \ _{:b:} P+\rho g y+\frac{1}{2}\rho v^2=constant\ \ \ _{:b:} v_1=\sqrt{2g(y_2-y_1)} Vibrations and Waves Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. F_s=-kx\ \ \ _{:b:} T_s=2\pi\sqrt{m/k}\ \ \ _{:b:} T_p=2\pi\sqrt{l/g}\ \ \ _{:b:} T=1/f\ \ \ _{:b:} v=f\lambda\ \ \ _{:b:} E_{SHO}=\frac{1}{2}mv^2+\frac{1}{2}kx^2 x(t)=A\cos(\omega t+\theta_0) v(t)=-\omega A\sin(\omega t+\theta_0) a(t)=-\omega^2A\cos(\omega t+\theta_0) F_{pendulum}=-mg\sin\theta\approx -mg\theta Sound Formulas v=f\lambda\ \ \ _{:b:} \beta \text{(in dB)} =10\log \frac{I}{I_0} f_{beats}=f_1-f_2 \lambda_1=2L (open tube) f_n=nf_1 (open tube) \lambda_1=4L (closed at one end) f_n=(2n+1)f_1 (closed at one end) f'=f/(1-\frac{v_{source}}{v_{sound}}) (source moving toward observer) f'=f/(1+\frac{v_{source}}{v_{sound}}) (source moving away from observer) Formulas with Summary Temperature and Thermal Expansion Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. T(K)=T(C^{\circ})+273.15 \Delta L=\alpha L_0\Delta T\ \ \ _{:b:} \Delta V=\beta V_0\Delta T PV=nRT=Nk_BT\ \ \ _{:b:} KE_{avg}=\frac{3}{2}k_BT (ideal gas) \ \ _{:b:} v_{rms}=\sqrt{3RT/M}=\sqrt{3k_BT/\mu}\ \ \ _{:b:} W=-P\Delta V (work done on a system) \ \ _{:b:} Heat Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. U=\frac{3}{2}nRT Q=mc\Delta T Q=mL_f (melting/freezing) Q=mL_V (vaporizing/condensing) H=(kA\Delta T)/L (Heat transfer) \ \ \ _{:b:} I=e\sigma AT^4 Thermodynamics Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. \Delta U=Q+W\ \ \ _{:b:} W=-P\Delta V\ \ \ _{:b:} (work done on a system) e=|W|/|Q_H|\ \ \ _{:b:} e=(T_H-T_C)/T_H\ \ \ _{:b:} \Delta Q=T\Delta S (T is constant) Electric Charge Forces and Fields Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. F=\frac{kq_1q_2}{r^2}=\frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}\ \ \ _{:bc:} \mathbf{E}=\frac{\mathbf{F}}{q}\ \ \ _{:bc:} \oint \mathbf{E}\cdot d\mathbf{A}=Q/\epsilon_0\ \ \ _{:c:} Electric Potential and Capacitance Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. U_E=qV=\frac{kq_1q_2}{r}=\frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}\ \ \ _{:bc:} E_{avg}=-V/d\ \ \ _{:b:} E=-\frac{dV}{dr}\ \ \ _{:c:} V=k(\frac{q_1}{r_1}+\frac{q_2}{r_2}+\frac{q_3}{r_3}+...)\ \ \ _{:b:} V=\frac{1}{4\pi\epsilon_0}\sum\frac{q_i}{r_i}\ \ \ _{:c:} C=Q/V\ \ \ _{:bc:} C=\epsilon_0A/d\ \ \ _{:bc:} U_C=\frac{1}{2}QV=\frac{1}{2}CV^2\ \ \ _{:bc:} Currents and Resistance Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. I_{avg}=\frac{\Delta Q}{\Delta t}\ \ \ _{:b:} I=\frac{dQ}{dt}\ \ \ _{:c:} V=IR\ \ \ _{:bc:} P=IV\ \ \ _{:bc:} R=\rho L/A\ \ \ _{:bc:} I=Nev_dA\ \ \ _{:c:} \mathbf{E}=\rho\mathbf{J}\ \ \ _{:c:} Circuits Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. R_{series}=R_1+R_2+R_3+...\ \ \ _{:b:} R_{series}=\sum_iR_i\ \ \ _{:c:} 1/R_{parallel}=1/R_1+1/R_2+1/R_3+...\ \ \ _{:b:} 1/R_{parallel}=\sum_i 1/R_i\ \ \ _{:c:} C_{parallel}=C_1+C_2+C_3+...\ \ \ _{:b:} C_{parallel}=\sum_iC_i\ \ \ _{:c:} 1/C_{series}=1/C_1+1/C_2+1/C_3+...\ \ \ _{:b:} 1/C_{series}=\sum_i 1/C_i\ \ \ _{:c:} V_C=V(1-e^{-t/RC}) (charging) Q_C=Q_0(1-e^{-t/RC}) (charging) V_C=V_0e^{-t/RC} (discharging) Q_C=Q_0e^{-t/RC} (discharging) \tau=RC (time constant) Magnetism Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. F_B=qvB\sin\theta\ \ \ _{:b:} \mathbf{F}_B=q\mathbf{v}\times\mathbf{B}\ \ \ _{:c:} F_B=BIL\sin\theta\ \ \ _{:b:} \mathbf{F}=\int Id\mathbf{l}\times\mathbf{B}\ \ \ _{:c:} \oint\mathbf{B}\cdot d\mathbf{l}=\mu_0 I\ \ \ _{:c:} B=\frac{\mu_0I}{2\pi r}\ \ \ _{:b:} d\mathbf{B}=\frac{\mu_0}{4\pi}\frac{Id\mathbf{l}\times\mathbf{r}}{r^3}\ \ \ _{:c:} B_s=\mu_0nI/l\ \ \ _{:c:} \tau=NIAB\sin\theta Electromagnetic Induction Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. \phi_m=BA\cos\theta\ \ \ _{:b:} \phi_m=\int\mathbf{B}\cdot d\mathbf{A}\ \ \ _{:c:} \mathcal{E}_{avg}=-\frac{\Delta\phi_m}{\Delta t}\ \ \ _{:b:} \mathcal{E}=\oint\mathbf{E}\cdot d\mathbf{l}=-\frac{d\theta_m}{dt}\ \ \ _{:c:} \mathcal{E}=Blv\ \ \ _{:b:} \frac{V_S}{V_P}=\frac{N_S}{N_P} (Transformer equation) \mathcal{E}=-L\frac{dI}{dt}\ \ \ _{:c:} U_L=\frac{1}{2}LI^2\ \ \ _{:c:} Electromagnetic Waves Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. \nabla\times\mathbf{B}=\mu_0\mathbf{J}+\mu_0\epsilon_0\frac{\partial \mathbf{E}}{\partial t} v=f\lambda\ \ \ _{:b:} U_{EM}=\frac{1}{2}\epsilon_0E^2+\frac{1}{2\mu_0}B^2=\epsilon_0E^2 \bar{I}=\frac{1}{2}\epsilon_0cE_0^2 P=\frac{\bar{I}}{c} (total absorption) P=\frac{2\bar{I}}{c} (total reflection) Reflection and Refraction Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. \theta_{incident}=\theta_{reflected} v=f\lambda\ \ \ _{:b:} f=\frac{R}{2}\ \ \ _{:b:} \frac{1}{d_i}+\frac{1}{d_o}=\frac{1}{f}\ \ \ _{:b:} m=\frac{h_i}{h_o}=-\frac{d_i}{d_o}\ \ \ _{:b:} n=\frac{c}{v}\ \ \ _{:b:} n_1\sin\theta_1=n_2\sin\theta_2\ \ \ _{:b:} \sin\theta_C=\frac{n_2}{n_1}\ \ \ _{:b:} Interference and Diffraction Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. d\sin\theta = m\lambda (constructive) \ \ \ _{:b:} d\sin\theta=(m+\frac{1}{2})\lambda (destructive) D\sin\theta=m\lambda,\ m\ne0 (single slit minima) d\sin\theta=m\lambda (diffraction grating maxima) I_{out}=I_{in}\cos^2\theta (polarization) \tan\theta_p=n_2/n_1 Optical Instruments Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. M=\frac{N}{f} (magnifying glass; eye focused at infinity) M=\frac{N}{f}+1 (magnifying glass; eye focuses at near point N) M=-\frac{f_o}{f_e} (telescope) \theta=1.22\lambda/D Special Relativity Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. \gamma=\frac{1}{\sqrt{1-v^2/c^2}} \Delta t=\gamma\Delta t_0 L=L_0/\gamma p=\gamma m_0 v E_0=m_0c^2 E=\gamma m_0c^2 E^2=p^2c^2+m_0^2c^4 v_3=\frac{v_1+v_2}{1+v_1v_2/c^2} Quantum Theory and the Atom Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. E=hf\ \ \ _{:b:} KE=hf-\phi (photoelectric effect) \ \ \ _{:b:} \lambda = h/p\ \ \ _{:b:} \lambda'=\lambda+\frac{h}{m_0c}(1-\cos\phi) \frac{1}{\lambda}=R(\frac{1}{2^2}-\frac{1}{n^2}),\ n\ge3 (Balmer series of H) \frac{1}{\lambda}=R(\frac{1}{1^2}-\frac{1}{n^2}),\ n\ge2 (Lyman series of H) \frac{1}{\lambda}=R(\frac{1}{3^2}-\frac{1}{n^2}),\ n\ge4 (Paschen series of H) E_n=-(13.6 eV)\frac{Z^2}{n^2} h/(2\pi)\le\Delta x\Delta p h/(2\pi)\le\Delta E\Delta t Nuclear Physics and Radioactivity Formulas Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a formula is on the AP Physics B, C or both B and C formula sheets. \Delta E=(\Delta m)c^2\ \ \ _{:b:} \alpha particle = 2 neutrons + 2 protons \beta -decay: n\rightarrow p+e^-+ neutrino N=N_0e^{-\lambda t} T_{1/2}=(\ln 2)/\lambda References Fundamental Constants Note: The _{:b:}\ ,\ _{:c:} and _{:bc:} symbols indicate that a constant is on the AP Physics B, C or both B and C formula sheets. Proton mass: m_p=1.67(26)\times 10^{-27}\ kg\ \ \ _{:bc:} Neutron mass: m_n=1.67(49)\times 10^{-27}\ kg\ \ \ _{:bc:} Electron mass: m_e=9.11\times10^{-31}\ kg\ \ \ _{:bc:} Avogadro's number: N_0=6.02\times10^{23}\ \ \ _{:bc:} Universal gas constant: R=8.31\ J/(mol\cdot K)\ \ \ _{:bc:} Boltzmann's constant: k_B=1.38\times 10^{-23}$\ J/K\ \ \ _{:bc:} Electron charge: e=1.60\times10^{-19}\ C\ \ \ _{:bc:} 1 electron volt: 1eV=1.6\times10^{-19}\ J\ \ \ _{:bc:} Speed of light in vacuum: c=3.00\times10^8\ m/s\ \ \ _{:bc:} Gravitation constant: G=6.67\times10^{-11}\ m^3/(kg\cdot s^2)\ \ \ _{:bc:} Acceleration due to gravity at Earth's surface: g=9.8\ m/s^2\ \ \ _{:bc:} 1 atomic mass unit: 1 u=1.66\times10^{-27}\ kg=931\ MeV/c^2\ \ \ _{:bc:} Planck's constant: h=6.63\times10^{-34}\ J\cdot s=4.14\times10^{-15}\ eV\cdot s\ \ \ _{:bc:} Planck's constant times c: hc=1.99\times10^{-25}\ J\cdot m=1.24\cdot 10^3\ eV\cdot nm\ \ \ _{:bc:} Vacuum permittivity: \epsilon_0=8.85\times10^{-12}\ C^2/(N\cdot m^2)\ \ \ _{:bc:} Coulomb's law constant: k=1/(4\pi\epsilon_0)=9.0\times10^9\ N\cdot m^2/C^2\ \ \ _{:bc:} Vacuum permeability: \mu_0=4\pi\times 10^{-7}\ (T\cdot m)/A\ \ \ _{:bc:} Magnetic constant: k'=\mu_0/4\pi=1\times10^{-7}\ (T\cdot m)/A\ \ \ _{:bc:} Atmospheric pressure: 1\ atm=1\times10^5\ N/m^2=1.0\times 10^5\ Pa\ \ \ _{:bc:} Stefan-Boltzmann constant: \sigma=5.67\times10^{-8}\ W/(m^2\cdot K^4) SI Units and their abbreviations Category:Browse